Large rescaling of the Higgs condensate: theoretical motivations and lattice results

In the Standard Model the Fermi constant is associated with the vacuum expectation value of the Higgs field, `the condensate', usually believed to be a cutoff-independent quantity. General arguments related to the `triviality' of $\Phi^4$ theory in 4 space-time dimensions suggest, however, a dramatic renormalization effect in the continuum limit that is clearly visible on the relatively large lattices available today. The result can be crucial for the Higgs phenomenology and in any context where spontaneous symmetry breaking is induced through scalar fields.Comment: LATTICE99(Higgs) 3 pages, 3 figure

Indications on the Higgs boson mass from lattice simulations

The `triviality' of $\Phi^4_4$ has been traditionally interpreted within perturbation theory where the prediction for the Higgs boson mass depends on the magnitude of the ultraviolet cutoff $\Lambda$. This approach crucially assumes that the vacuum field and its quantum fluctuations rescale in the same way. The results of the present lattice simulation, confirming previous numerical indications, show that this assumption is not true. As a consequence, large values of the Higgs mass $m_H$ can coexist with the limit $\Lambda\to \infty$. As an example, by extrapolating to the Standard Model our results obtained in the Ising limit of the one-component theory, one can obtain a value as large as $m_H=760 \pm 21$ GeV, independently of $\Lambda$.Comment: 3 pages, 2 figures, Lattice2003(higgs

An alternative heavy Higgs mass limit

After commenting on the present value of the Higgs particle mass from radiative corrections, we explore the phenomenological implications of an alternative, non-perturbative renormalization of the scalar sector where the mass of the Higgs particle does not represent a measure of observable interactions at the Higgs mass scale. In this approach the Higgs particle could be very heavy, even heavier than 1 TeV, and remain nevertheless a relatively narrow resonance.Comment: 17 pages. Version accepted for publication in Journal of Physics

First lattice evidence for a non-trivial renormalization of the Higgs condensate

General arguments related to ``triviality'' predict that, in the broken phase of $(\lambda\Phi^4)_4$ theory, the condensate re-scales by a factor $Z_{\phi}$ different from the conventional wavefunction-renormalization factor, $Z_{prop}$. Using a lattice simulation in the Ising limit we measure $Z_{\phi}=m^2 \chi$ from the physical mass and susceptibility and $Z_{prop}$ from the residue of the shifted-field propagator. We find that the two $Z$'s differ, with the difference increasing rapidly as the continuum limit is approached. Since $Z_{\phi}$ affects the relation of to the Fermi constant it can sizeably affect the present bounds on the Higgs mass.Comment: 10 pages, 3 figures, 1 table, Latex2